Simplify - square root of -4-3 square root of 9+ square root of -81

$- \sqrt{- 4} - 3 \sqrt{9} + \sqrt{- 81}$

Step 1

Simplify each term.

Rewrite $- 4$ as $- 1 (4)$ .

$- \sqrt{- 1 (4)} - 3 \sqrt{9} + \sqrt{- 81}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$- (\sqrt{- 1} \cdot \sqrt{4}) - 3 \sqrt{9} + \sqrt{- 81}$

Rewrite $\sqrt{- 1}$ as $i$ .

$- (i \cdot \sqrt{4}) - 3 \sqrt{9} + \sqrt{- 81}$

Rewrite $4$ as $2^{2}$ .

$- (i \cdot \sqrt{2^{2}}) - 3 \sqrt{9} + \sqrt{- 81}$

Pull terms out from under the radical, assuming positive real numbers.

$- (i \cdot 2) - 3 \sqrt{9} + \sqrt{- 81}$

Move $2$ to the left of $i$ .

$- (2 \cdot i) - 3 \sqrt{9} + \sqrt{- 81}$

Multiply $2$ by $- 1$ .

$- 2 i - 3 \sqrt{9} + \sqrt{- 81}$

Rewrite $9$ as $3^{2}$ .

$- 2 i - 3 \sqrt{3^{2}} + \sqrt{- 81}$

Pull terms out from under the radical, assuming positive real numbers.

$- 2 i - 3 \cdot 3 + \sqrt{- 81}$

Multiply $- 3$ by $3$ .

$- 2 i - 9 + \sqrt{- 81}$

Rewrite $- 81$ as $- 1 (81)$ .

$- 2 i - 9 + \sqrt{- 1 (81)}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$- 2 i - 9 + \sqrt{- 1} \cdot \sqrt{81}$

Rewrite $\sqrt{- 1}$ as $i$ .

$- 2 i - 9 + i \cdot \sqrt{81}$

Rewrite $81$ as $9^{2}$ .

$- 2 i - 9 + i \cdot \sqrt{9^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$- 2 i - 9 + i \cdot 9$

Move $9$ to the left of $i$ .

$- 2 i - 9 + 9 i$

Step 2

Add $- 2 i$ and $9 i$ .

$- 9 + 7 i$